Virginia SOL 8.NS.1.b
The Standard
Use rational approximations (to the nearest hundredth) of irrational numbers to compare, order, and locate values on a number line. Radicals may include both positive and negative square roots of values from 0 to 400 yielding an irrational number.
Virginia Standards of Learning for Mathematics · The student will compare and order real numbers and determine the relationships between real numbers.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students estimate irrational square roots as decimals rounded to the nearest hundredth. They compare positive and negative values, arrange mixed sets, and place each value on a number line.
What Mastery Looks Like
- Given values such as √50, -√20, 6.9, and -4.6, students find decimal estimates and order them correctly. They place each value accurately on a number line and explain comparisons using nearby perfect squares.
Common Misconceptions
- Students may treat √50 as 25 or assume every square root is a whole number. They may confuse -√20 with √-20 or forget that values farther left are smaller when comparing negatives. Some round the radicand before finding its square root.
How to Assess It
- Exit ticket: Approximate -√18 and √10 to the nearest hundredth, then order them with -3.9 and 3.2 and plot all four values.
Lesson moves
Ways to Teach It
Give students radical cards, decimal cards, and a floor number line; they match each radical to its approximation and place both cards.
Ask, “Which is greater, -√30 or -5.4?” Students write an estimate and explain how the negative sign affects the comparison.
Play a card-sort race: teams approximate six radicals, arrange them from least to greatest, then check with calculators.
For square parks with side lengths 5, 8, and 10 meters, students approximate each diagonal and rank the shortcuts.
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Printable 8.NS.1.b Worksheet
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